Well, in geometry class, עִגּוּל is the area of the circle, but מַעֲגָּל the line around it: . In real life they are very similar, but notice that the second is used in many stock phrases like מַגְגַּל־חַשְׁמַלִּי "electric circuit" or מַגְגַּל־קְסָמִים "vicious circle".
I'm a little confused, your diagram has עיגול as the inside but your text says its the outside. If the diagram is right, it makes sense that עיגול would mean a circle like a dic and מעגל would mean something like the people are standing in a circle. I can also see how saying that sign is a circle could use either.
Sorry typo :-( Since הוּא מְגַגֵּל means he googles, מַעֲגַל־חַשְׁמַלִּי electric circuit and מַעֲגַל־קְסָמִים vicious circle are correct. Biblical מַעֲגָל meant the tracks made by a cart, and thus in Psalm 23.3 figuratively premade tracks to follow. The meaning circumference is based on its use in 1Samuel, where it means something like circled wagon train. While an autistic mathematician might read it as you proposed, the interpretation as a righteous circuit (or how about a modern in the range of righteousness) instead of a vicious one seems as nice as the original meaning to me.